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Math lesson plan · 10th grade (Year 11 in England) · 30 minutes

Conditional probability and independence

Statistics and probability

CCSS HSS.CP.A.3CCSS HSS.CP.A.4CCSS HSS.CP.B.6England: GCSE Higher Probability

Objective and success criteria

Students will: Conditional probability and independence.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Tree diagrams and Venn diagrams; Two-way tables

Leads to: Use P(A | B) = P(A and B) ÷ P(B); Test for independence using a two-way table

Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Tree diagrams and Venn diagrams; Two-way tables). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A bag has 6 red and 7 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 36/169Prompt: Multiply along the branches of the tree diagram.
  2. A two-way table: Year 7 — cats 17, dogs 10; Year 8 — cats 12, dogs 18. How many Year 8 students are there? → 30Prompt: Find the row or column you need.
  3. In a class of 23, 14 play guitar, 8 play piano and 4 play both. One student is chosen at random. What is the probability they play both? Simplest form. → 4/23Prompt: Draw a Venn diagram. Put the 'both' number in the overlap first.

Hook · 3 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Conditional probability and independence. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Survey: Likes science & is in Club — 19; Likes science & not in Club — 11; Doesn't like science & in Club — 5; neither — 12. Given a student is in the Club, what is the probability they like science? Simplest form.
  • Step 1: Club members: 19 + 5 = 24
  • Step 2: P = 19/24
  • Answer: 19/24
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Survey: Likes science & is in Club — 13; Likes science & not in Club — 15; Doesn't like science & in Club — 25; neither — 15. Given a student is in the Club, what is the probability they like science? Simplest form. → 13/38Prompt: 'Given' means only look at the Club members.
  2. P(A) = 0.5, P(B) = 0.2 and P(A and B) = 0.1. Are A and B independent? (Yes / No) → YesPrompt: A and B are independent if P(A and B) = P(A) × P(B).

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Survey: Likes science & is in Club — 8; Likes science & not in Club — 25; Doesn't like science & in Club — 11; neither — 23. Given a student is in the Club, what is the probability they like science? Simplest form. → 8/19Prompt: 'Given' means only look at the Club members.
  2. P(A) = 0.2, P(B) = 0.4 and P(A and B) = 0.08. Are A and B independent? (Yes / No) → YesPrompt: A and B are independent if P(A and B) = P(A) × P(B).

Watch out for

  • Forgetting to put data in order before finding the median.
  • Reading a bar's height wrongly when the scale goes up in 2s or 5s.

Support and stretch

Support

  • Review first: Tree diagrams and Venn diagrams.
  • Use concrete materials: squared paper for charts.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Use P(A | B) = P(A and B) ÷ P(B); Test for independence using a two-way table.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.

Free lesson plan from eurekami.com/lesson-plan-builder

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Conditional probability and independence

Name

Date

Score/ 6

  1. Question 1

    Survey: Likes science & is in Club — 19; Likes science & not in Club — 9; Doesn't like science & in Club — 13; neither — 22. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  2. Question 2

    P(A) = 0.3, P(B) = 0.5 and P(A and B) = 0.15. Are A and B independent?

    • A. Yes
    • B. No

  3. Question 3

    Survey: Likes science & is in Club — 15; Likes science & not in Club — 8; Doesn't like science & in Club — 13; neither — 10. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  4. Question 4

    P(A) = 0.2, P(B) = 0.25 and P(A and B) = 0.05. Are A and B independent?

    • A. Yes
    • B. No

  5. Question 5

    Survey: Likes science & is in Club — 14; Likes science & not in Club — 14; Doesn't like science & in Club — 14; neither — 25. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  6. Question 6

    P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.25. Are A and B independent?

    • A. Yes
    • B. No

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Answer key: Conditional probability and independence

  1. 1. 19/32

  2. 2. A. Yes

  3. 3. 15/28

  4. 4. A. Yes

  5. 5. 1/2

  6. 6. B. No